Print-friendly page

Translating Word Problems: Keywords (page 1 of 2)

Sections: Keywords, Worked examples

The hardest thing about doing word problems is taking the English problem and translating it into math. Usually, once you get the math equation, you're fine. The actual math involved is often fairly simple. But actually getting the equation can seem nearly impossible. What follows is a list of hints and helps. To really learn how to do word problems, you'll just have to practice, practice, practice.

The first step to effectively working word problems is to read the problem entirely. Don't try to start solving anything when you've only read half a sentence. Try to get a feel for the whole problem, and try to see what information you have, and what you still need.

The second step is to work in an organized manner. Label variables with what they stand for, draw and label pictures neatly, and explain your reasoning as you go along. And you need to determine what the problem is actually asking for. You need to do this for two reasons:

1. Working clearly will help you think clearly, and
2. figuring out what you need will help you translate your final answer back into English.

(Regarding (2) above, I can tell you from experience: It's really frustrating (and embarassing) to spend fifteen minutes solving a word problem on a test, only to realize at the end that you no longer have any idea what "x" stands for, so you have to do the whole problem over again. I did this on a calculus test -- thank heavens it was a short test! -- and, trust me, you don't want to do this to yourself!)

The third step is to look for "key" words. Certain words indicate certain mathematical operations. Below is a partial list. Copyright © Elizabeth Stapel 2006-2008 All Rights Reserved

Addition	increased by more than combined, together total of sum added to
Subtraction	decreased by minus, less difference between/of less than, fewer than
Multiplication	of times, multiplied by product of increased/decreased by a   factor of (this type can   involve both addition or   subtraction and   multiplication!)
Division	per, a out of ratio of, quotient of percent (divide by 100)
Equals	is, are, was, were, will be gives, yields sold for

Note that "per" means "divided by", as in "I drove 90 miles on three gallons of gas, so I got 30 miles per gallon". Also, "a" sometimes means "divided by", as in "When I tanked up, I paid $3.90 for three gallons, so the gas was $1.30 a gallon".

Let me emphasize that "less than" is backwards in the English from what it is in the math. If you need to translate "1.5 less than x", the temptation is to write "1.5 – x". Do not do this. If you put a "real world" situation in, you'll see how this is wrong: "He makes $1.50 an hour less than me." You do not figure his wage by subtracting your wage from $1.50. Instead, you subtract $1.50 from your wage. Just remember; the "less than" construction is backwards.

Also note that order is important in the "quotient/ratio of" and "difference between/of" constructions. If a problems says "the ratio of x and y", it means "x divided by y", not "y divided by x". If the problem says "the difference of x and y", it means "x – y", not "y – x".

Now we need to learn to extract the keywords from the word problems.

Top  |  1 | 2  |  Return to Index  Next >>

  Copyright © 2006-2008  Elizabeth Stapel   |   About   |   Terms of Use

 Feedback   |   Error?